The Tor Browser: comparison mfbt/double-conversion/fixed-dtoa.cc

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+:cbef4576ea24
+// Copyright 2010 the V8 project authors. All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     * Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//     * Redistributions in binary form must reproduce the above
+//       copyright notice, this list of conditions and the following
+//       disclaimer in the documentation and/or other materials provided
+//       with the distribution.
+//     * Neither the name of Google Inc. nor the names of its
+//       contributors may be used to endorse or promote products derived
+//       from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+#include <math.h>
+#include "fixed-dtoa.h"
+#include "ieee.h"
+namespace double_conversion {
+// Represents a 128bit type. This class should be replaced by a native type on
+// platforms that support 128bit integers.
+class UInt128 {
+public:
+UInt128() : high_bits_(0), low_bits_(0) { }
+UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { }
+void Multiply(uint32_t multiplicand) {
+uint64_t accumulator;
+accumulator = (low_bits_ & kMask32) * multiplicand;
+uint32_t part = static_cast<uint32_t>(accumulator & kMask32);
+accumulator >>= 32;
+accumulator = accumulator + (low_bits_ >> 32) * multiplicand;
+low_bits_ = (accumulator << 32) + part;
+accumulator >>= 32;
+accumulator = accumulator + (high_bits_ & kMask32) * multiplicand;
+part = static_cast<uint32_t>(accumulator & kMask32);
+accumulator >>= 32;
+accumulator = accumulator + (high_bits_ >> 32) * multiplicand;
+high_bits_ = (accumulator << 32) + part;
+ASSERT((accumulator >> 32) == 0);
+}
+void Shift(int shift_amount) {
+ASSERT(-64 <= shift_amount && shift_amount <= 64);
+if (shift_amount == 0) {
+return;
+} else if (shift_amount == -64) {
+high_bits_ = low_bits_;
+low_bits_ = 0;
+} else if (shift_amount == 64) {
+low_bits_ = high_bits_;
+high_bits_ = 0;
+} else if (shift_amount <= 0) {
+high_bits_ <<= -shift_amount;
+high_bits_ += low_bits_ >> (64 + shift_amount);
+low_bits_ <<= -shift_amount;
+} else {
+low_bits_ >>= shift_amount;
+low_bits_ += high_bits_ << (64 - shift_amount);
+high_bits_ >>= shift_amount;
+}
+}
+// Modifies *this to *this MOD (2^power).
+// Returns *this DIV (2^power).
+int DivModPowerOf2(int power) {
+if (power >= 64) {
+int result = static_cast<int>(high_bits_ >> (power - 64));
+high_bits_ -= static_cast<uint64_t>(result) << (power - 64);
+return result;
+} else {
+uint64_t part_low = low_bits_ >> power;
+uint64_t part_high = high_bits_ << (64 - power);
+int result = static_cast<int>(part_low + part_high);
+high_bits_ = 0;
+low_bits_ -= part_low << power;
+return result;
+}
+}
+bool IsZero() const {
+return high_bits_ == 0 && low_bits_ == 0;
+}
+int BitAt(int position) {
+if (position >= 64) {
+return static_cast<int>(high_bits_ >> (position - 64)) & 1;
+} else {
+return static_cast<int>(low_bits_ >> position) & 1;
+}
+}
+private:
+static const uint64_t kMask32 = 0xFFFFFFFF;
+// Value == (high_bits_ << 64) + low_bits_
+uint64_t high_bits_;
+uint64_t low_bits_;
+};
+static const int kDoubleSignificandSize = 53;  // Includes the hidden bit.
+static void FillDigits32FixedLength(uint32_t number, int requested_length,
+Vector<char> buffer, int* length) {
+for (int i = requested_length - 1; i >= 0; --i) {
+buffer[(*length) + i] = '0' + number % 10;
+number /= 10;
+}
+*length += requested_length;
+}
+static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) {
+int number_length = 0;
+// We fill the digits in reverse order and exchange them afterwards.
+while (number != 0) {
+int digit = number % 10;
+number /= 10;
+buffer[(*length) + number_length] = '0' + digit;
+number_length++;
+}
+// Exchange the digits.
+int i = *length;
+int j = *length + number_length - 1;
+while (i < j) {
+char tmp = buffer[i];
+buffer[i] = buffer[j];
+buffer[j] = tmp;
+i++;
+j--;
+}
+*length += number_length;
+}
+static void FillDigits64FixedLength(uint64_t number, int requested_length,
+Vector<char> buffer, int* length) {
+const uint32_t kTen7 = 10000000;
+// For efficiency cut the number into 3 uint32_t parts, and print those.
+uint32_t part2 = static_cast<uint32_t>(number % kTen7);
+number /= kTen7;
+uint32_t part1 = static_cast<uint32_t>(number % kTen7);
+uint32_t part0 = static_cast<uint32_t>(number / kTen7);
+FillDigits32FixedLength(part0, 3, buffer, length);
+FillDigits32FixedLength(part1, 7, buffer, length);
+FillDigits32FixedLength(part2, 7, buffer, length);
+}
+static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) {
+const uint32_t kTen7 = 10000000;
+// For efficiency cut the number into 3 uint32_t parts, and print those.
+uint32_t part2 = static_cast<uint32_t>(number % kTen7);
+number /= kTen7;
+uint32_t part1 = static_cast<uint32_t>(number % kTen7);
+uint32_t part0 = static_cast<uint32_t>(number / kTen7);
+if (part0 != 0) {
+FillDigits32(part0, buffer, length);
+FillDigits32FixedLength(part1, 7, buffer, length);
+FillDigits32FixedLength(part2, 7, buffer, length);
+} else if (part1 != 0) {
+FillDigits32(part1, buffer, length);
+FillDigits32FixedLength(part2, 7, buffer, length);
+} else {
+FillDigits32(part2, buffer, length);
+}
+}
+static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) {
+// An empty buffer represents 0.
+if (*length == 0) {
+buffer[0] = '1';
+*decimal_point = 1;
+*length = 1;
+return;
+}
+// Round the last digit until we either have a digit that was not '9' or until
+// we reached the first digit.
+buffer[(*length) - 1]++;
+for (int i = (*length) - 1; i > 0; --i) {
+if (buffer[i] != '0' + 10) {
+return;
+}
+buffer[i] = '0';
+buffer[i - 1]++;
+}
+// If the first digit is now '0' + 10, we would need to set it to '0' and add
+// a '1' in front. However we reach the first digit only if all following
+// digits had been '9' before rounding up. Now all trailing digits are '0' and
+// we simply switch the first digit to '1' and update the decimal-point
+// (indicating that the point is now one digit to the right).
+if (buffer[0] == '0' + 10) {
+buffer[0] = '1';
+(*decimal_point)++;
+}
+}
+// The given fractionals number represents a fixed-point number with binary
+// point at bit (-exponent).
+// Preconditions:
+//   -128 <= exponent <= 0.
+//   0 <= fractionals * 2^exponent < 1
+//   The buffer holds the result.
+// The function will round its result. During the rounding-process digits not
+// generated by this function might be updated, and the decimal-point variable
+// might be updated. If this function generates the digits 99 and the buffer
+// already contained "199" (thus yielding a buffer of "19999") then a
+// rounding-up will change the contents of the buffer to "20000".
+static void FillFractionals(uint64_t fractionals, int exponent,
+int fractional_count, Vector<char> buffer,
+int* length, int* decimal_point) {
+ASSERT(-128 <= exponent && exponent <= 0);
+// 'fractionals' is a fixed-point number, with binary point at bit
+// (-exponent). Inside the function the non-converted remainder of fractionals
+// is a fixed-point number, with binary point at bit 'point'.
+if (-exponent <= 64) {
+// One 64 bit number is sufficient.
+ASSERT(fractionals >> 56 == 0);
+int point = -exponent;
+for (int i = 0; i < fractional_count; ++i) {
+if (fractionals == 0) break;
+// Instead of multiplying by 10 we multiply by 5 and adjust the point
+// location. This way the fractionals variable will not overflow.
+// Invariant at the beginning of the loop: fractionals < 2^point.
+// Initially we have: point <= 64 and fractionals < 2^56
+// After each iteration the point is decremented by one.
+// Note that 5^3 = 125 < 128 = 2^7.
+// Therefore three iterations of this loop will not overflow fractionals
+// (even without the subtraction at the end of the loop body). At this
+// time point will satisfy point <= 61 and therefore fractionals < 2^point
+// and any further multiplication of fractionals by 5 will not overflow.
+fractionals *= 5;
+point--;
+int digit = static_cast<int>(fractionals >> point);
+buffer[*length] = '0' + digit;
+(*length)++;
+fractionals -= static_cast<uint64_t>(digit) << point;
+}
+// If the first bit after the point is set we have to round up.
+if (((fractionals >> (point - 1)) & 1) == 1) {
+RoundUp(buffer, length, decimal_point);
+}
+} else {  // We need 128 bits.
+ASSERT(64 < -exponent && -exponent <= 128);
+UInt128 fractionals128 = UInt128(fractionals, 0);
+fractionals128.Shift(-exponent - 64);
+int point = 128;
+for (int i = 0; i < fractional_count; ++i) {
+if (fractionals128.IsZero()) break;
+// As before: instead of multiplying by 10 we multiply by 5 and adjust the
+// point location.
+// This multiplication will not overflow for the same reasons as before.
+fractionals128.Multiply(5);
+point--;
+int digit = fractionals128.DivModPowerOf2(point);
+buffer[*length] = '0' + digit;
+(*length)++;
+}
+if (fractionals128.BitAt(point - 1) == 1) {
+RoundUp(buffer, length, decimal_point);
+}
+}
+}
+// Removes leading and trailing zeros.
+// If leading zeros are removed then the decimal point position is adjusted.
+static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) {
+while (*length > 0 && buffer[(*length) - 1] == '0') {
+(*length)--;
+}
+int first_non_zero = 0;
+while (first_non_zero < *length && buffer[first_non_zero] == '0') {
+first_non_zero++;
+}
+if (first_non_zero != 0) {
+for (int i = first_non_zero; i < *length; ++i) {
+buffer[i - first_non_zero] = buffer[i];
+}
+*length -= first_non_zero;
+*decimal_point -= first_non_zero;
+}
+}
+bool FastFixedDtoa(double v,
+int fractional_count,
+Vector<char> buffer,
+int* length,
+int* decimal_point) {
+const uint32_t kMaxUInt32 = 0xFFFFFFFF;
+uint64_t significand = Double(v).Significand();
+int exponent = Double(v).Exponent();
+// v = significand * 2^exponent (with significand a 53bit integer).
+// If the exponent is larger than 20 (i.e. we may have a 73bit number) then we
+// don't know how to compute the representation. 2^73 ~= 9.5*10^21.
+// If necessary this limit could probably be increased, but we don't need
+// more.
+if (exponent > 20) return false;
+if (fractional_count > 20) return false;
+*length = 0;
+// At most kDoubleSignificandSize bits of the significand are non-zero.
+// Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero
+// bits:  0..11*..0xxx..53*..xx
+if (exponent + kDoubleSignificandSize > 64) {
+// The exponent must be > 11.
+//
+// We know that v = significand * 2^exponent.
+// And the exponent > 11.
+// We simplify the task by dividing v by 10^17.
+// The quotient delivers the first digits, and the remainder fits into a 64
+// bit number.
+// Dividing by 10^17 is equivalent to dividing by 5^17*2^17.
+const uint64_t kFive17 = UINT64_2PART_C(0xB1, A2BC2EC5);  // 5^17
+uint64_t divisor = kFive17;
+int divisor_power = 17;
+uint64_t dividend = significand;
+uint32_t quotient;
+uint64_t remainder;
+// Let v = f * 2^e with f == significand and e == exponent.
+// Then need q (quotient) and r (remainder) as follows:
+//   v            = q * 10^17       + r
+//   f * 2^e      = q * 10^17       + r
+//   f * 2^e      = q * 5^17 * 2^17 + r
+// If e > 17 then
+//   f * 2^(e-17) = q * 5^17        + r/2^17
+// else
+//   f  = q * 5^17 * 2^(17-e) + r/2^e
+if (exponent > divisor_power) {
+// We only allow exponents of up to 20 and therefore (17 - e) <= 3
+dividend <<= exponent - divisor_power;
+quotient = static_cast<uint32_t>(dividend / divisor);
+remainder = (dividend % divisor) << divisor_power;
+} else {
+divisor <<= divisor_power - exponent;
+quotient = static_cast<uint32_t>(dividend / divisor);
+remainder = (dividend % divisor) << exponent;
+}
+FillDigits32(quotient, buffer, length);
+FillDigits64FixedLength(remainder, divisor_power, buffer, length);
+*decimal_point = *length;
+} else if (exponent >= 0) {
+// 0 <= exponent <= 11
+significand <<= exponent;
+FillDigits64(significand, buffer, length);
+*decimal_point = *length;
+} else if (exponent > -kDoubleSignificandSize) {
+// We have to cut the number.
+uint64_t integrals = significand >> -exponent;
+uint64_t fractionals = significand - (integrals << -exponent);
+if (integrals > kMaxUInt32) {
+FillDigits64(integrals, buffer, length);
+} else {
+FillDigits32(static_cast<uint32_t>(integrals), buffer, length);
+}
+*decimal_point = *length;
+FillFractionals(fractionals, exponent, fractional_count,
+buffer, length, decimal_point);
+} else if (exponent < -128) {
+// This configuration (with at most 20 digits) means that all digits must be
+// 0.
+ASSERT(fractional_count <= 20);
+buffer[0] = '\0';
+*length = 0;
+*decimal_point = -fractional_count;
+} else {
+*decimal_point = 0;
+FillFractionals(significand, exponent, fractional_count,
+buffer, length, decimal_point);
+}
+TrimZeros(buffer, length, decimal_point);
+buffer[*length] = '\0';
+if ((*length) == 0) {
+// The string is empty and the decimal_point thus has no importance. Mimick
+// Gay's dtoa and and set it to -fractional_count.
+*decimal_point = -fractional_count;
+}
+return true;
+}
+}  // namespace double_conversion

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comparison: mfbt/double-conversion/fixed-dtoa.cc

mfbt/double-conversion/fixed-dtoa.cc